Saint Basil Academy Mathematics Department Mrs. Theresa Hartey

Honors Algebra II Summer Review Packet Directions: This packet is required if you are registered for Honors Algebra II for the 2016-2017 school year. Please show all work to earn full credit for this assignment. Circle your final answers. This packet needs to be turned in on the first full day of classes and will count as your first two homework assignment grades. I look forward to studying mathematics with you in the fall. We will work together to problem solve, think critically, analyze data, and communicate mathematically. It will be great fun! In some of the sections you will find reference information as a reminder of how to complete the exercises, but you may need to search for things in a textbook or on the Internet if you cannot remember how to complete some of the exercises from previous coursework. A few high quality resources you may find useful include:

1) http://www.purplemath.com 2) https://www.khanacademy.org 3) http://www.ck12.org/algebra/

In the meantime, have a wonderful summer! God bless, Mrs. Hartey J

Solving Equations

Examples: You should not require any reminder on how to solve the first two examples, but may need the example provided to refresh your memory for the three that follow.

Practice: Solve & check. If there is no solution, write no solution.

1) 7+ 7x = − x + 4( )+8 x − 4( )

2) −12 6x −12( ) = −12 4x + 4( )

3) 23x − 6 =12

4) 3 6x − 7 +10 = 8

Solving Inequalities

You should not require any reminder on how to solve the first four examples, but may need the example provided to refresh your memory for the three that follow.

Practice: Solve and graph on a number line.

5) 5 x +3( ) ≤ 2 x − 4( )−3 x +1( )

6) x + 5( )+ 2 7− x( )+15< 1

432x − 44( )

7) 4+ 5x > 24 or 16+ x ≤17

8) 3 x + 2( ) < 5x −11< 3x + 7

9) 6x +15 −3≥14

10) 5 x − 2 + 7 <17

Linear Equations

Writing Linear Equations Practice: Write the linear equation in slope-intercept form. Slope-intercept form: y =mx + b

11) slope= − 34

, y-intercept = 2

12) through: 4,1( ) and −3,−1( )

13) through: −1, 4( ) , parallel to 3x − y = 5

14) through: 0,3( ) , parallel to 2x − 4y = 7

15) through: −4,−3( ) , perpendicular to 2x − 5y =10

16) 2,−6( ) , perpendicular to −3x − 7y = 2

Modeling with Linear Equations Practice: Write a linear equation to model the situation. Be sure to define your variables. A Hawaiian fruit company is studying the sales of a pineapple sauce to see if the product is to be continued. At the end of its first year, profits on the product were $30,000. At the end of the fourth year, profits were $66,000. Assume the relationship between years on the market and profit in linear.

17) Write an equation to model the situation.

18) Use the equation to predict the profit at the end of 7 years.

Systems of Linear Equations: Practice: Solve the system of linear equations by the specified method.

19) Solve by elimination.

3x + 2y = −54x −3y =16"#$

20) Solve by substitution.

5x − y =13x − 4y = −5"#$

21) Solve by graphing. x + y =13x − y = −5"#$

Attach your work on graph paper.

Functions Evaluating Functions Examples:

Practice: Evaluate for

22)

23)

24)

25) c −14

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26) k −2( )

27) h 12!

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m(x) = 2x2 − x + 2m(2) = 2(2)2 − (2)+ 2m(2) = 8

r(x) = −x3 + x +1r(−4) = −(−4)3 + (−4)+1r(−4) = 61

c(x) = −16x2 − 4x + 2 , h(x) = x4 − 2x , k(x) = 2x3 + 5x2

h(−2)

k(3)

c 12!

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Polynomials Simplifying Polynomials Practice: Simplify completely.

28) 236x2 − 9x +3( )

29) 5x +1( ) 3x − 2( )

30) 4x −3( ) 4x +3( )

31) 5x − 7( )2

32) x − 2( )3

33) 4x − 5( ) x +3( ) 4x + 5( ) x −3( )

34) 3x2 − 4x +1( ) 2x + 5( )

35)

€

4 7x − 5( ) − 3 6 − 9x( )

36) 4x − 5( ) x +3( )+ 4x − 5( ) x −3( )

37)

€

18 − 24x−6

Factoring Polynomials Examples: Factor.

a) GCF:

b) Difference of Squares:

c) Product/Sum: d) By Grouping: e) ac-method:

f) Substitution:

1) Let n = x2 so 4x4 −12x2 + 5= 4n2 −12n+ 5= 2n− 5( ) 2n−1( ) = 2x2 − 5( ) 2x2 −1( )

2) Let n = x + 2 so 3 x + 2( )2 −8 x + 2( )+ 4 = 3n2 −8n+ 4 = 3n− 2( ) n− 2( )

= 3 x + 2( )− 2"# $% x + 2( )− 2"# $%= 3x + 4( ) x( ) = 3x2 + 4x Practice: Factor completely.

38)

39)

40)

41)

42)

43)

4x3y+ 6x2y− 2x = 2x 2x2y+3xy−1( )4x2 − 9 = 2x −3( )(2x +3)x2 + 2x −15= (x + 5)(x −3)x3 − 4x2 + 2x −8 = x2 x − 4( )+ 2(x − 4) = (x2 + 2)(x − 4)

2x2 − 7x +3= 2x2 − x − 6x +3= x(2x −1)−3(2x −1) = (x −3)(2x −1)

5a2b+10ab3

x2 − 25

x2 + 6x

1−16x2

6x3 − 9x2 + 2x −3

5x2 − 20

44)

45)

46)

47)

48) 2 x −1( )2 − 9 x −1( )− 5

49) 2x4 − 5x2 +3

x2 −8x +15

5x2 − 7x + 2

2x2 − 2x − 24

6x2 − x −1

Solving Quadratic Equations Examples: Solve the following quadratic equations.

a) Solve by factoring:

b) Solve by Square Root Property:

x −8( )2 = 36⇒ x −8( )2 = ± 36 ⇒ x −8 = ±6⇒ x = 8± 6⇒ x =14or x = 2

14,2{ }

c) Solve by Quadratic Formula:

Practice: Solve.

50) 51)

x2 + 2x −15= 0x −3( ) x + 5( ) = 0x −3= 0 or x + 5= 0x = 3 or x = −53,−5{ }

2x2 −3x − 9 = 0

x =−(−3) ± (−3)2 − 4(2)(−9)

2(2)=3± 814

=3± 94

x = 124= 3

or

x = − 64= −

32

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$$

3,− 32

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x2 − 4x −8 = 0

x =−(− 4) ± (− 4)2 − 4(1)(−8)

2(1)=4± 482

=4± 4 32

x = 2+ 2 3or

x = 2− 2 3

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2+ 2 3 , 2− 2 3{ }

x2 + 7x +12 = 0 5x2 =10x

52)

53) x + 6( )2 =1

54) 3x − 4( )2 =16

55)

56)

57)

2x2 + x =15 −x2 + 2x +10 = 0

x2 −16 = 0

2x2 −3x −3= 0